Geometry of the Unit Sphere in Polynomial Spaces (Springerbriefs in Mathematics)

Ferrer, Jesús/ García, Domingo/ Maestre, Manuel

Springer International Publishing AG（2023/03発売）

• 製本 Paperback:紙装版/ペーパーバック版／ページ数 137 p.
• 商品コード 9783031236754

Full Description

This brief presents a global perspective on the geometry of spaces of polynomials. Its particular focus is on polynomial spaces of dimension 3, providing, in that case, a graphical representation of the unit ball. Also, the extreme points in the unit ball of several polynomial spaces are characterized. Finally, a number of applications to obtain sharp classical polynomial inequalities are presented.

The study performed is the first ever complete account on the geometry of the unit ball of polynomial spaces. Nowadays there are hundreds of research papers on this topic and our work gathers the state of the art of the main and/or relevant results up to now. This book is intended for a broad audience, including undergraduate and graduate students, junior and senior researchers and it also serves as a source book for consultation. In addition to that, we made this work visually attractive by including in it over 50 original figures in order to help in the understanding of allthe results and techniques included in the book.

Contents

Chapter. 1. Introduction.- Chapter. 2. Polynomials of degree.- Chapter. 3. Spaces of trinomials.- Chapter. 4. Polynomials on nonsymmetric convex bodies.- Chapter. 5. Sequence Banach spaces.- Chapter. 6. Polynomials with the hexagonal and octagonal norms.- Chapter. 7. Hilbert spaces.- Chapter. 8. Banach spaces.- Chapter. 9. Applications.